Question

A kindergarten teacher gave 114 sweets to children in the kindergarten. Each 4-year old child received 2 sweets and Each 5-year old child received 3 sweets. The 5-year old children received 6 more sweets than the 4-year old children. Find the total number of children in the kindergarten.

Answer 1

$\textsf{Let the Number of 4 - Year Old Children in the Kindergarten be : P}$

$\textsf{Let the Number of 5 - Year Old Children in the Kindergarten be : Q}$

$\textsf{Given : Number of Sweets given by Teacher to each 4 - Year Old Child = 2}$

$\implies \mathsf{Total\;Number\;of\;Sweets\;received\;by\;4 - Year\;Old\;Children = (2 \times P)}$

$\textsf{Given : Number of Sweets given by Teacher to each 5 - Year Old Child = 3}$

$\implies \mathsf{Total\;Number\;of\;Sweets\;received\;by\;5 - Year\;Old\;Children = (3 \times Q)}$

$\textsf{Given : 5 - year old children received 6 More sweets than 4 - year old children}$

$\implies \mathsf{3Q = 2P + 6\;-----\;[1]}$

$\textsf{Given : The Teacher gave a Total of 114 Sweets to all the Children}$

$\implies \mathsf{2P + 3Q = 114\;-----\;[2]}$

$\textsf{Substituting Equation [1] in Equation [2], We get :}$

$\implies \textsf{2P + 2P + 6 = 114}$

$\implies \textsf{4P = 114 - 6}$

$\implies \textsf{4P = 108}$

$\implies \textsf{P = 27}$

$\textsf{Substituting P = 27 in Equation [1], We get :}$

$\implies \textsf{3Q = 2(27) + 6}$

$\implies \textsf{3Q = 54 + 6}$

$\implies \textsf{3Q = 60}$

$\implies \textsf{Q = 20}$

$\implies \textsf{Number of 4 - Year Old Children in the Kindergarten = 27}$

$\implies \textsf{Number of 5 - Year Old Children in the Kindergarten = 20}$

$\implies \textsf{Total Number of Children in the Kindergarten = (27 + 20)}$

$\underline{\bf{Answer}} : \textsf{The Total Number of Children in the Kindergarten = 47}$